光学子波变换及其在图象处理中的应用
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摘要
本文系统地阐述了子波变换的发展动态及基本理论。详细分析总结了光学
子波变换的特性、构成方法及应用范围。深入研究了光学子波变换的实现技术及
其在图象特征提取和纹理图象分割等方面的应用。
利用角度复合体全息技术构造了光学二维Haar子波变换系统。利甩Haar
子波的复合，并行提取了二值图象的不同局域特征。提出了Roberts算子可以作
为子波函数，利用其旋转反对称性能克服Haar子波的局限性，用来提取图象的
任意取向的边沿。模拟和实验的结果证明了上述观点。
提出了联合子波变换相关器（JWTC）。克服了在频谱域中构成子波变换时
所常遇到的困难。并提出了空分复用JWTC，它可以对图象进行并行多尺度、多
子波分析以及对不同特征的并行提取和综合。
提出了光波衍射过程是一种广义的子波变换。把子波理论中的子波概念推
广到非带通函数族，将惠更斯球面子波以及菲涅耳衍射的脉冲响应函数改写为
子波的形式。以其衍射距离的变化实现子波理论中扩因子的缩放。然后，根据周
期物体的泰伯效应提出了一种纹理分割的新技术。理论分析与初步的实验结果
验证了这种空间分布图象处理技术的可行性。
提出了基于光学子波变换的多通道纹理图象分割技术。以人类视觉信息处
理理论中的多通道滤波机制为基础，把光学子波变换与神经网络以及模糊聚类
技术相结合，形成了一种具备一定智能性质的图象处理技术。构建了光电混合型
纹理分割实验系统，用光学子波变换实现快速图象变换，神经网络和模糊聚类算
法进行图象特征识别。利用这一系统对典型纹理图象、岩石表面、和航拍市区照
片的纹理分割进行了应用研究。获得了较好的计算机模拟结果和实验结果。
为了使系统的结构更紧凑有效，提出并研制了一种同时具有滤波、分束、成
象等功能的二元光学新器件。利用这种被称作“光学视网膜”的器件将能够一次
获得多种尺度、多种取向的子波变换结果。
The development of Wavelet Transform (WT) and its fundamental theory are
systematically described in this dissertation. The properties, implementations, and
applications of the Optical Wavelet Transform (OWT) are analysed and discussed
in detail. The techniques for realization of OWT and applications in image feature
extraction and texture segmentation are explored thoroughly.
An optical system for two-dimensional Haar WT is constructed by using an
angular multiplexing volume hologram technique. Different local features of binary
image are extracted simultaneously by using the multiplexing Haar wavelets. The
Roberts operator is proposed to be used as wavelet. Roberts wavelet can overcome
the limitations of Haar wavelet and can be used for extracting any edges of different
orientations of an input image because it is rotational anti-symmetricity. Simula-
tions and experiments are performed to confirm the validity.
A joint wavelet-transform correlator (JWTC) is proposed. The difficulties
generally encountered for the implementation in the frequency domain of OWT can
be overcomed by the proposed JWTC. A spatial-division-multiplexing JWTC is al-
so designed, which can analyze an image with multi-scale and multi-wavelet, ex-
tract and synthesize different features of an input image simultaneously.
Diffraction is treated as wavelet transform in a broad sense. The wavelet con-
cept of the wavelet theory is extended to non-dandpass family of functions. The
Huygens spherical wavelet and the impulse response of Fresnel diffraction are re-
written in the form of wavelet. The diffraction distance performs the dilation factor
of wavelet theory. Then, a new technique for texture segmentation is proposed
based on the Talbot effect of the periodic object. Theoretical analysis and primitive
experimental results verify the feasibility of spatial distributed image processing
techniques.
A scheme for texture segmentation with multi-channel OWT is proposed.
This scheme is based on the multi-channel filtering mechanism of human vision in-
formation processing theory. The OWT, neural network (NN) and fuzzy c-mean
clustering algorithm (FCM), are studied and synthesised to form an intelligent liii-
age processing technique to some extent. Based on this approach, a hybrid texture
segmentation experimental system is designed and implemented, where the OWT is
used for realizing the fast image transform. The NN and the FCM are used for im-
age feature recognition. The applications of this system in the segmentation of tex-
ture of the typical texture image, rock surface, and bird-view photograph of a city,
etc are studied. Fine results of experiments and computer simulations are provided.
In order to make the system more compact and robust, we proposed and fabri-
cated a novel binary optical element named "optical retina" for the reason that it
has the functions of filtering, beam-splitting, and imaging, etc simultaneously.
The OWT of an input image with multi-scale and multi-orientation can be obtained
in one operation with this element.
子波变换的特性、构成方法及应用范围。深入研究了光学子波变换的实现技术及
其在图象特征提取和纹理图象分割等方面的应用。
利用角度复合体全息技术构造了光学二维Haar子波变换系统。利甩Haar
子波的复合，并行提取了二值图象的不同局域特征。提出了Roberts算子可以作
为子波函数，利用其旋转反对称性能克服Haar子波的局限性，用来提取图象的
任意取向的边沿。模拟和实验的结果证明了上述观点。
提出了联合子波变换相关器（JWTC）。克服了在频谱域中构成子波变换时
所常遇到的困难。并提出了空分复用JWTC，它可以对图象进行并行多尺度、多
子波分析以及对不同特征的并行提取和综合。
提出了光波衍射过程是一种广义的子波变换。把子波理论中的子波概念推
广到非带通函数族，将惠更斯球面子波以及菲涅耳衍射的脉冲响应函数改写为
子波的形式。以其衍射距离的变化实现子波理论中扩因子的缩放。然后，根据周
期物体的泰伯效应提出了一种纹理分割的新技术。理论分析与初步的实验结果
验证了这种空间分布图象处理技术的可行性。
提出了基于光学子波变换的多通道纹理图象分割技术。以人类视觉信息处
理理论中的多通道滤波机制为基础，把光学子波变换与神经网络以及模糊聚类
技术相结合，形成了一种具备一定智能性质的图象处理技术。构建了光电混合型
纹理分割实验系统，用光学子波变换实现快速图象变换，神经网络和模糊聚类算
法进行图象特征识别。利用这一系统对典型纹理图象、岩石表面、和航拍市区照
片的纹理分割进行了应用研究。获得了较好的计算机模拟结果和实验结果。
为了使系统的结构更紧凑有效，提出并研制了一种同时具有滤波、分束、成
象等功能的二元光学新器件。利用这种被称作“光学视网膜”的器件将能够一次
获得多种尺度、多种取向的子波变换结果。
The development of Wavelet Transform (WT) and its fundamental theory are
systematically described in this dissertation. The properties, implementations, and
applications of the Optical Wavelet Transform (OWT) are analysed and discussed
in detail. The techniques for realization of OWT and applications in image feature
extraction and texture segmentation are explored thoroughly.
An optical system for two-dimensional Haar WT is constructed by using an
angular multiplexing volume hologram technique. Different local features of binary
image are extracted simultaneously by using the multiplexing Haar wavelets. The
Roberts operator is proposed to be used as wavelet. Roberts wavelet can overcome
the limitations of Haar wavelet and can be used for extracting any edges of different
orientations of an input image because it is rotational anti-symmetricity. Simula-
tions and experiments are performed to confirm the validity.
A joint wavelet-transform correlator (JWTC) is proposed. The difficulties
generally encountered for the implementation in the frequency domain of OWT can
be overcomed by the proposed JWTC. A spatial-division-multiplexing JWTC is al-
so designed, which can analyze an image with multi-scale and multi-wavelet, ex-
tract and synthesize different features of an input image simultaneously.
Diffraction is treated as wavelet transform in a broad sense. The wavelet con-
cept of the wavelet theory is extended to non-dandpass family of functions. The
Huygens spherical wavelet and the impulse response of Fresnel diffraction are re-
written in the form of wavelet. The diffraction distance performs the dilation factor
of wavelet theory. Then, a new technique for texture segmentation is proposed
based on the Talbot effect of the periodic object. Theoretical analysis and primitive
experimental results verify the feasibility of spatial distributed image processing
techniques.
A scheme for texture segmentation with multi-channel OWT is proposed.
This scheme is based on the multi-channel filtering mechanism of human vision in-
formation processing theory. The OWT, neural network (NN) and fuzzy c-mean
clustering algorithm (FCM), are studied and synthesised to form an intelligent liii-
age processing technique to some extent. Based on this approach, a hybrid texture
segmentation experimental system is designed and implemented, where the OWT is
used for realizing the fast image transform. The NN and the FCM are used for im-
age feature recognition. The applications of this system in the segmentation of tex-
ture of the typical texture image, rock surface, and bird-view photograph of a city,
etc are studied. Fine results of experiments and computer simulations are provided.
In order to make the system more compact and robust, we proposed and fabri-
cated a novel binary optical element named "optical retina" for the reason that it
has the functions of filtering, beam-splitting, and imaging, etc simultaneously.
The OWT of an input image with multi-scale and multi-orientation can be obtained
in one operation with this element.
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